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Problem of the Week 823

Odd Pythagoreans

Prove that there are no odd positive integers x, y, and z which satisfy the Pythagorean relation (x+y)2 + (x+z)2 = (y+z)2.

Source: This problem appears in Ross Honsberger's recent book, "From Erdõs to Kiev", and is due to Johann Walter from Aachen, Germany. It was suggested by Loren Larson who is speaking next week at Macalester on Fermat's Two Square Theorem.

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998